I have a proposition for the page Proving "for all" statements.
There is a more general approach/view, which generalize induction and the articles in the subsection Prove the result for some cases and deduce it for the rest.
It is the following: If you have to show a statement 
it is useful to exploit the structure of the set 
.
If there are for example some operations 
acting on such that
you can write every 
as 
with a special point 
and you can show:
1)